Maximal L p -regularity for evolution equations governed by non-autonomous forms in weighted spaces

We consider the maximal regularity for non-autonomous Cauchy problem u′(t)+A(t)u(t)=f(t),t-a.e.,u(0)=u0.Each operator A(t) arises from a time depending on a sesquilinear form a(t) on a Hilbert space H with a constant domain V. We show maximal Lp−regularity result in temporally weighted Lp-spaces for 2<p<∞ and other regularity properties for the solution of the previous problem under sufficient regularity assumption on the forms and the initial value u0, which is significantly weaker than those from previous contributions. Our results are motivated by boundary value problems.